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In many cases a scalar field can lead to accelerated expansion incosmological models. This paper contains mathematical results on this subjectparticularly on type I Bianchi space-time. In this paper, global existence tothe coupled Einstein-scalar field system which rules the dynamics of a kind ofpure matter in the presence of a scalar field and cosmological constant isproven.

Einstein-Scalar Field System with a cosmological constant on the type I Bianchi space-time